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Accueil > Interactions > Interdisciplinaires > Health Care and Biology : Mass transfer in bio-medical processes

Health Care and Biology : Mass transfer in bio-medical processes    fr

The team "Partial Differential Equations and Control Theory" has developed collaborations in these three areas:
- the simulation of blood flows in the human vascular system,
- the numerical rheology of the blood and
- the mass transfer from the vascular system (through the blood) to the surrounding tissues.

These different collaborations share many similarities and common toolchains and software are being setup.

Mass transfer in bio-medical processes

- Research team : partial differential equations and control theory
- Contact : Laurent Navoret

Mass transfers between different media intervene in many bio-medical processes. Moreover, quantifying such transfers is often a key question to predict the development or the remission of one disease. However, these mechanisms involve a lot of agents (molecules, cells), that interact through numerous mechanical/chemical reactions at different space and time scales. Faced to such complex systems, elaborating relevant mathematical models for mass transfer is made extremely difficult. That is why few mathematical and numerical works deal with the chemical/mechanical processes of mass transfer. Such studies could yet result in improved computer-aided prognosis. Mass transfer raises also many computational questions. As many bio-mechanisms, the mass transfer time scale is often much smaller than the disease development. Thus, to simulate such multi-scale phenomena, we need to devise efficient numerical methods that are not submitted to stringent restrictions related to the finer time scale (i.e. the cardiac cycle time scale). Finally, as in the atherosclerosis disease, mass transfer is followed by the aggregation of matter and then to the deformation of the media, that can influence the mass transfer itself (for instance via the blood-structure interaction). Therefore, such coupled system need specific mathematical and numerical treatment.

We have recently started to work on mass transfer in bio-medical processes in the framework of the european project ARTreat. In collaboration with mathematicians of the Paris Descartes Univ. and the Paris Sud Univ and physicians (IFC-CNR in Pisa, Cambridge Neuroscience in Cambridge Univ.), we are interested in the atherosclerosis disease, when lipids aggregate in the arterial wall and then could bring forth heart attacks or cerebrovascular accidents. We develop different mathematical models using age-dependent PDE, that link the lipid accumulation in the sub-endothelial layer to the blood flow. This work is first intended to help the physicians to identify the underlying processes of the transfer mechanisms (molecules adhesion, absorption site repartition) and then to relate these processes to the macroscopic boundary conditions of the interface blood/arterial wall.

Dernière mise à jour le 15-11-2011